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 A068140 Smaller of two consecutive numbers each divisible by a cube greater than one. 19
 80, 135, 296, 343, 351, 375, 512, 567, 624, 728, 783, 944, 999, 1160, 1215, 1375, 1376, 1431, 1592, 1624, 1647, 1808, 1863, 2024, 2079, 2240, 2295, 2375, 2400, 2456, 2511, 2624, 2672, 2727, 2888, 2943, 3087, 3104, 3159, 3320, 3375, 3429, 3536, 3591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Cubeful numbers with cubeful successors. This is to cubes as A068781 is to squares. 1375 is the smallest of three consecutive numbers divisible by a cube, since 1375 = 5^3 * 11 and 1376 = 2^5 * 43 and 1377 = 3^4 * 17. What is the smallest of four consecutive numbers divisible by a cube? Of n consecutive numbers divisible by a cube? - Jonathan Vos Post, Sep 18 2007 22624 is the smallest of four consecutive numbers each divisible by a cube, with factorizations 2^5 * 7 * 101, 5^3 * 181, 2 * 3^3 * 419, and 11^3 * 17. - D. S. McNeil, Dec 10 2010 18035622 is the smallest of five consecutive numbers each divisible by a cube. 4379776620 is the smallest of six consecutive numbers each divisible by a cube. 1204244328624 is the smallest of seven consecutive numbers each divisible by a cube. - Donovan Johnson, Dec 13 2010 The sequence is the union, over all pairs of distinct primes (p,q), of numbers == 0 mod p^3 and == -1 mod q^3 or vice versa. - Robert Israel, Aug 13 2018 The asymptotic density of this sequence is 1 - 2/zeta(3) + Product_{p prime} (1 - 2/p^3) = 1 - 2 * A088453 + A340153 = 0.013077991848467056243... - Amiram Eldar, Feb 16 2021 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA {k such that k is in A046099 and k+1 is in A046099}. - Jonathan Vos Post, Sep 18 2007 EXAMPLE 343 is a term as 343 = 7^3 and 344= 2^3 * 43. MAPLE isA068140 := proc(n) isA046099(n) and isA046099(n+1) ; end proc: for n from 1 to 4000 do if isA068140(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Dec 08 2015 MATHEMATICA a = b = 0; Do[b = Max[ Transpose[ FactorInteger[n]] []]; If[a > 2 && b > 2, Print[n - 1]]; a = b, {n, 2, 5000}] Select[Range[2, 6000], Max[Transpose[FactorInteger[ # ]][]] > 2 && Max[Transpose[FactorInteger[ # + 1]][]] > 2 &] (* Jonathan Vos Post, Sep 18 2007 *) SequencePosition[Table[If[AnyTrue[Rest[Divisors[n]], IntegerQ[Surd[#, 3]]&], 1, 0], {n, 3600}], {1, 1}][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 18 2020 *) CROSSREFS Cf. A046099, A063528, A068781, A068782, A068783, A068784, A088453, A122692, A174113, A340152, A340153. Sequence in context: A062376 A223087 A261549 * A365867 A349307 A349308 Adjacent sequences: A068137 A068138 A068139 * A068141 A068142 A068143 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Feb 22 2002 EXTENSIONS Edited and extended by Robert G. Wilson v, Mar 02 2002 Title edited, cross-references added by Matthew Vandermast, Dec 09 2010 Definition clarified by Harvey P. Dale, Apr 18 2020 STATUS approved

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Last modified September 29 00:22 EDT 2023. Contains 365739 sequences. (Running on oeis4.)